BBY - Detail Report

Quick Overview

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)	Binomial IV (Period)	Yahoo IV (Period)	1σ Lower (68.27%)	1σ Upper	2σ Lower (95.45%)	2σ Upper
Daily	3.16%	2.65%	2.72%	3.08%	2.94%	3.02%	62.61	66.40	60.80	68.38
Weekly	7.25%	7.08%	7.11%	7.27%	6.47%	6.66%	60.44	68.79	56.66	73.38
Monthly	15.84%	17.50%	16.15%	15.73%	13.46%	13.86%	56.36	73.77	49.26	84.40
Quarterly	29.21%	33.56%	26.18%	26.79%	23.32%	24.00%	51.07	81.41	40.45	102.79
Annual	—	—	—	—	46.63%	48.00%	40.45	102.79	25.37	163.86
Option Time Horizon	—	—	—	—	17.94%	18.46%	53.89	77.15	45.04	92.30

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $64.48 | Strike (K): $65.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.2500 (Bid $3.9500 / Ask $4.5500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 5.72% | Binomial IV (Annual): 46.63% (CRR binomial tree, American, n=20 steps) | BS IV: 46.64% (European Black-Scholes) | Yahoo IV (Annual): 48.00% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2025-12-16	$0.9500
2025-09-18	$0.9500
2025-06-18	$0.9500
2025-03-25	$0.9500
2024-12-17	$0.9400
2024-09-19	$0.9400
2024-06-20	$0.9400
2024-03-20	$0.9400
2023-12-11	$0.9200
2023-09-18	$0.9200
2023-06-14	$0.9200
2023-03-22	$0.9200
2022-12-12	$0.8800
2022-09-19	$0.8800
2022-06-13	$0.8800
2022-03-23	$0.8800
2021-12-13	$0.7000
2021-09-13	$0.7000
2021-06-16	$0.7000
2021-03-17	$0.7000
2020-12-14	$0.5500
2020-09-14	$0.5500
2020-06-10	$0.5500
2020-03-18	$0.5500
2019-12-16	$0.5000
2019-09-18	$0.5000
2019-06-12	$0.5000
2019-03-19	$0.5000
2018-12-10	$0.4500
2018-09-17	$0.4500
2018-06-13	$0.4500
2018-03-21	$0.4500
2017-12-06	$0.3400
2017-09-18	$0.3400
2017-06-13	$0.3400
2017-03-20	$0.3400
2016-12-06	$0.2800
2016-09-09	$0.2800
2016-06-10	$0.2800
2016-03-15	$0.7300
2015-12-08	$0.2300
2015-09-11	$0.2300
2015-06-09	$0.2300
2015-03-20	$0.7400
2014-12-09	$0.1900
2014-09-09	$0.1900
2014-06-10	$0.1700
2014-03-18	$0.1700
2013-12-06	$0.1700
2013-09-06	$0.1700
2013-06-07	$0.1700
2013-03-19	$0.1700
2012-12-07	$0.1700
2012-09-07	$0.1700
2012-06-08	$0.1600
2012-04-17	$0.1600
2011-12-29	$0.1600
2011-09-30	$0.1600
2011-06-30	$0.1500
2011-04-12	$0.1500
2010-12-31	$0.1500
2010-10-01	$0.1500
2010-07-01	$0.1400
2010-04-13	$0.1400
2009-12-31	$0.1400
2009-10-02	$0.1400
2009-07-02	$0.1400
2009-04-14	$0.1400
2009-01-02	$0.1400
2008-10-03	$0.1400
2008-07-03	$0.1300
2008-04-21	$0.1300
2008-01-07	$0.1300
2007-10-04	$0.1300
2007-07-06	$0.1000
2007-04-23	$0.1000
2006-12-28	$0.1000
2006-09-29	$0.1000
2006-06-29	$0.0800
2006-04-18	$0.0800
2005-12-29	$0.0800
2005-09-30	$0.0800
2005-06-30	$0.0733
2005-04-18	$0.0733
2005-01-03	$0.0733
2004-10-04	$0.0733
2004-07-02	$0.0667
2004-04-19	$0.0667
2004-01-05	$0.0667
2003-11-14	$0.2000

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.22. Further, an Excess Kurtosis of 12.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.36%	72	0.70%	0.70%
-9.36% to -6.99%	84	0.82%	1.52%
-6.99% to -4.62%	289	2.82%	4.33%
-4.62% to -2.25%	1101	10.72%	15.06%
-2.25% to 0.11%	3941	38.39%	53.45%
0.11% to 2.48%	3220	31.37%	84.81%
2.48% to 4.85%	1061	10.34%	95.15%
4.85% to 7.22%	282	2.75%	97.90%
7.22% to 9.59%	104	1.01%	98.91%
Greater than 9.59%	112	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.04%	3.27%	80.27%	68.27%
±2σ	-6.20%	6.43%	95.23%	95.45%
±3σ	-9.36%	9.59%	98.21%	99.73%

Descriptive Statistics

Mean	0.114%
Standard Error	0.031%
Median	0.000%
Mode	0.000%
Standard Deviation	3.157%
Sample Variance	9.965%
Kurtosis	12.43
Skewness	-0.22
Range	66.056%
Minimum	-38.783%
Maximum	27.273%
Count	10266

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.291%	4943	48.15%	1.103%
Negative	-2.116%	4798	46.74%	-0.989%
Zero	0.000%	525	5.11%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.12%
20	1 Month	3.69%
60	1 Quarter	3.34%
250	1 Year	3.49%
750	3 Years	2.87%
1,250	5 Years	3.08%
2,500	10 Years	3.01%
5,000	20 Years	3.19%
12,500	50 Years	3.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.71. Further, an Excess Kurtosis of 146.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.39%	0	0.00%	0.00%
-4.39% to -2.40%	0	0.00%	0.00%
-2.40% to -0.41%	0	0.00%	0.00%
-0.41% to 1.58%	1219	11.87%	11.87%
1.58% to 3.57%	5387	52.47%	64.34%
3.57% to 5.56%	2214	21.56%	85.91%
5.56% to 7.55%	800	7.79%	93.70%
7.55% to 9.54%	354	3.45%	97.15%
9.54% to 11.53%	128	1.25%	98.39%
Greater than 11.53%	165	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.92%	6.22%	88.46%	68.27%
±2σ	-1.74%	8.88%	96.21%	95.45%
±3σ	-4.39%	11.53%	98.39%	99.73%

Descriptive Statistics

Mean	3.569%
Standard Error	0.026%
Median	2.891%
Mode	2.857%
Standard Deviation	2.653%
Sample Variance	7.037%
Kurtosis	146.28
Skewness	6.71
Range	89.195%
Minimum	0.279%
Maximum	89.474%
Count	10267

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.569%	10267	100.00%	3.569%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.58. Further, an Excess Kurtosis of 35.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.10%	70	0.68%	0.68%
-8.10% to -6.07%	106	1.03%	1.71%
-6.07% to -4.03%	331	3.22%	4.94%
-4.03% to -1.99%	1154	11.24%	16.18%
-1.99% to 0.05%	3724	36.27%	52.45%
0.05% to 2.08%	3257	31.72%	84.17%
2.08% to 4.12%	1134	11.05%	95.22%
4.12% to 6.16%	318	3.10%	98.31%
6.16% to 8.20%	99	0.96%	99.28%
Greater than 8.20%	74	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.67%	2.76%	79.02%	68.27%
±2σ	-5.39%	5.48%	95.21%	95.45%
±3σ	-8.10%	8.20%	98.60%	99.73%

Descriptive Statistics

Mean	0.047%
Standard Error	0.027%
Median	0.000%
Mode	0.000%
Standard Deviation	2.717%
Sample Variance	7.384%
Kurtosis	35.36
Skewness	1.58
Range	79.994%
Minimum	-22.449%
Maximum	57.545%
Count	10267

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.941%	4936	48.08%	0.933%
Negative	-1.937%	4696	45.74%	-0.886%
Zero	0.000%	635	6.18%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.35. Further, an Excess Kurtosis of 3.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.19%	9	0.42%	0.42%
-21.19% to -15.75%	27	1.27%	1.69%
-15.75% to -10.31%	83	3.89%	5.58%
-10.31% to -4.87%	234	10.98%	16.56%
-4.87% to 0.57%	751	35.24%	51.81%
0.57% to 6.01%	673	31.58%	83.39%
6.01% to 11.45%	222	10.42%	93.81%
11.45% to 16.89%	84	3.94%	97.75%
16.89% to 22.32%	28	1.31%	99.06%
Greater than 22.32%	20	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.68%	7.82%	76.87%	68.27%
±2σ	-13.93%	15.07%	94.27%	95.45%
±3σ	-21.19%	22.32%	98.64%	99.73%

Descriptive Statistics

Mean	0.569%
Standard Error	0.157%
Median	0.258%
Mode	0.000%
Standard Deviation	7.252%
Sample Variance	52.595%
Kurtosis	3.83
Skewness	0.35
Range	88.640%
Minimum	-39.344%
Maximum	49.296%
Count	2131

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.593%	1094	51.34%	2.871%
Negative	-4.873%	1007	47.26%	-2.303%
Zero	0.000%	30	1.41%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.71%
12	1 Quarter	6.50%
52	1 Year	8.07%
156	3 Years	6.74%
260	5 Years	7.27%
520	10 Years	7.15%
1,040	20 Years	7.53%
2,600	50 Years	9.34%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.38. Further, an Excess Kurtosis of 22.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.49%	0	0.00%	0.00%
-11.49% to -6.18%	0	0.00%	0.00%
-6.18% to -0.88%	0	0.00%	0.00%
-0.88% to 4.43%	307	14.40%	14.40%
4.43% to 9.74%	1073	50.33%	64.73%
9.74% to 15.05%	421	19.75%	84.47%
15.05% to 20.36%	181	8.49%	92.96%
20.36% to 25.67%	78	3.66%	96.62%
25.67% to 30.98%	37	1.74%	98.36%
Greater than 30.98%	35	1.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.66%	16.82%	86.82%	68.27%
±2σ	-4.41%	23.90%	96.11%	95.45%
±3σ	-11.49%	30.98%	98.36%	99.73%

Descriptive Statistics

Mean	9.743%
Standard Error	0.153%
Median	7.714%
Mode	5.882%
Standard Deviation	7.079%
Sample Variance	50.113%
Kurtosis	22.08
Skewness	3.38
Range	92.122%
Minimum	1.562%
Maximum	93.684%
Count	2132

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.743%	2132	100.00%	9.743%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 9.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.29%	7	0.33%	0.33%
-21.29% to -15.96%	20	0.94%	1.27%
-15.96% to -10.63%	79	3.71%	4.97%
-10.63% to -5.30%	258	12.10%	17.07%
-5.30% to 0.03%	755	35.41%	52.49%
0.03% to 5.36%	682	31.99%	84.47%
5.36% to 10.69%	211	9.90%	94.37%
10.69% to 16.02%	76	3.56%	97.94%
16.02% to 21.35%	24	1.13%	99.06%
Greater than 21.35%	20	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.08%	7.14%	77.81%	68.27%
±2σ	-14.18%	14.24%	94.98%	95.45%
±3σ	-21.29%	21.35%	98.73%	99.73%

Descriptive Statistics

Mean	0.030%
Standard Error	0.154%
Median	-0.156%
Mode	0.000%
Standard Deviation	7.107%
Sample Variance	50.505%
Kurtosis	9.83
Skewness	1.20
Range	99.427%
Minimum	-33.019%
Maximum	66.408%
Count	2132

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.236%	1014	47.56%	2.490%
Negative	-4.822%	1088	51.03%	-2.461%
Zero	0.000%	30	1.41%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.50. Further, an Excess Kurtosis of 1.54 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.93%	2	0.41%	0.41%
-44.93% to -33.05%	3	0.61%	1.02%
-33.05% to -21.17%	17	3.47%	4.49%
-21.17% to -9.29%	68	13.88%	18.37%
-9.29% to 2.58%	179	36.53%	54.90%
2.58% to 14.46%	129	26.33%	81.22%
14.46% to 26.34%	53	10.82%	92.04%
26.34% to 38.22%	27	5.51%	97.55%
38.22% to 50.09%	6	1.22%	98.78%
Greater than 50.09%	6	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.25%	18.42%	75.71%	68.27%
±2σ	-29.09%	34.26%	94.08%	95.45%
±3σ	-44.93%	50.09%	98.37%	99.73%

Descriptive Statistics

Mean	2.584%
Standard Error	0.715%
Median	0.925%
Mode	0.000%
Standard Deviation	15.837%
Sample Variance	250.819%
Kurtosis	1.54
Skewness	0.50
Range	117.149%
Minimum	-48.692%
Maximum	68.457%
Count	490

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.689%	257	52.45%	7.180%
Negative	-9.834%	229	46.73%	-4.596%
Zero	0.000%	4	0.82%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	13.98%
12	1 Year	17.37%
36	3 Years	14.58%
60	5 Years	15.73%
120	10 Years	15.85%
240	20 Years	16.62%
600	50 Years	21.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.99. Further, an Excess Kurtosis of 15.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.86%	0	0.00%	0.00%
-27.86% to -14.73%	0	0.00%	0.00%
-14.73% to -1.61%	0	0.00%	0.00%
-1.61% to 11.52%	82	16.70%	16.70%
11.52% to 24.64%	232	47.25%	63.95%
24.64% to 37.76%	96	19.55%	83.50%
37.76% to 50.89%	47	9.57%	93.08%
50.89% to 64.01%	19	3.87%	96.95%
64.01% to 77.14%	7	1.43%	98.37%
Greater than 77.14%	8	1.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.14%	42.14%	87.58%	68.27%
±2σ	-10.36%	59.64%	95.93%	95.45%
±3σ	-27.86%	77.14%	98.37%	99.73%

Descriptive Statistics

Mean	24.639%
Standard Error	0.790%
Median	19.795%
Mode	11.048%
Standard Deviation	17.499%
Sample Variance	306.214%
Kurtosis	15.32
Skewness	2.99
Range	160.701%
Minimum	6.667%
Maximum	167.368%
Count	491

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.639%	491	100.00%	24.639%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.27. Further, an Excess Kurtosis of 5.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.31%	0	0.00%	0.00%
-48.31% to -36.20%	2	0.41%	0.41%
-36.20% to -24.08%	20	4.07%	4.48%
-24.08% to -11.97%	77	15.68%	20.16%
-11.97% to 0.15%	156	31.77%	51.93%
0.15% to 12.26%	158	32.18%	84.11%
12.26% to 24.38%	49	9.98%	94.09%
24.38% to 36.49%	18	3.67%	97.76%
36.49% to 48.61%	6	1.22%	98.98%
Greater than 48.61%	5	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.01%	16.30%	75.36%	68.27%
±2σ	-32.16%	32.45%	95.52%	95.45%
±3σ	-48.32%	48.61%	98.98%	99.73%

Descriptive Statistics

Mean	0.147%
Standard Error	0.729%
Median	-0.371%
Mode	-20.000%
Standard Deviation	16.154%
Sample Variance	260.967%
Kurtosis	5.42
Skewness	1.27
Range	135.658%
Minimum	-40.512%
Maximum	95.146%
Count	491

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.240%	236	48.06%	5.883%
Negative	-11.089%	254	51.73%	-5.736%
Zero	0.000%	1	0.20%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.17. Further, an Excess Kurtosis of 2.56 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -79.88%	0	0.00%	0.00%
-79.88% to -57.97%	0	0.00%	0.00%
-57.97% to -36.07%	5	3.05%	3.05%
-36.07% to -14.16%	27	16.46%	19.51%
-14.16% to 7.74%	62	37.80%	57.32%
7.74% to 29.65%	39	23.78%	81.10%
29.65% to 51.55%	17	10.37%	91.46%
51.55% to 73.46%	9	5.49%	96.95%
73.46% to 95.36%	3	1.83%	98.78%
Greater than 95.36%	2	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.46%	36.95%	76.83%	68.27%
±2σ	-50.67%	66.16%	95.73%	95.45%
±3σ	-79.88%	95.37%	98.78%	99.73%

Descriptive Statistics

Mean	7.744%
Standard Error	2.281%
Median	2.221%
Mode	-55.914%
Standard Deviation	29.207%
Sample Variance	853.022%
Kurtosis	2.56
Skewness	1.17
Range	189.140%
Minimum	-55.914%
Maximum	133.226%
Count	164

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.622%	87	53.05%	14.653%
Negative	-14.716%	77	46.95%	-6.909%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	21.89%
12	3 Years	25.02%
20	5 Years	26.79%
40	10 Years	27.09%
80	20 Years	29.00%
200	50 Years	39.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.76. Further, an Excess Kurtosis of 3.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.68%	0	0.00%	0.00%
-50.68% to -25.51%	0	0.00%	0.00%
-25.51% to -0.34%	0	0.00%	0.00%
-0.34% to 24.83%	33	20.00%	20.00%
24.83% to 50.00%	76	46.06%	66.06%
50.00% to 75.17%	28	16.97%	83.03%
75.17% to 100.34%	14	8.48%	91.52%
100.34% to 125.51%	7	4.24%	95.76%
125.51% to 150.68%	4	2.42%	98.18%
Greater than 150.68%	3	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	16.44%	83.56%	81.82%	68.27%
±2σ	-17.12%	117.12%	94.55%	95.45%
±3σ	-50.68%	150.68%	98.18%	99.73%

Descriptive Statistics

Mean	49.999%
Standard Error	2.613%
Median	40.224%
Mode	20.550%
Standard Deviation	33.559%
Sample Variance	1126.239%
Kurtosis	3.58
Skewness	1.76
Range	185.633%
Minimum	12.262%
Maximum	197.895%
Count	165

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	49.999%	165	100.00%	49.999%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.01. Further, an Excess Kurtosis of 3.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -78.74%	0	0.00%	0.00%
-78.74% to -59.10%	0	0.00%	0.00%
-59.10% to -39.47%	6	3.64%	3.64%
-39.47% to -19.84%	32	19.39%	23.03%
-19.84% to -0.21%	49	29.70%	52.73%
-0.21% to 19.42%	49	29.70%	82.42%
19.42% to 39.05%	17	10.30%	92.73%
39.05% to 58.68%	9	5.45%	98.18%
58.68% to 78.31%	1	0.61%	98.79%
Greater than 78.31%	2	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.39%	25.96%	75.76%	68.27%
±2σ	-52.56%	52.14%	95.76%	95.45%
±3σ	-78.74%	78.31%	98.79%	99.73%

Descriptive Statistics

Mean	-0.211%
Standard Error	2.038%
Median	-1.504%
Mode	-56.985%
Standard Deviation	26.175%
Sample Variance	685.151%
Kurtosis	3.10
Skewness	1.01
Range	183.814%
Minimum	-56.985%
Maximum	126.829%
Count	165

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.467%	78	47.27%	9.675%
Negative	-18.751%	87	52.73%	-9.887%
Zero	0.000%	0	0.00%	0.000%

BBY Deep Analytical Report